{"id":625,"date":"2021-04-20T01:14:42","date_gmt":"2021-04-19T17:14:42","guid":{"rendered":"https:\/\/blog.cruciferslab.net\/?p=625"},"modified":"2024-03-08T11:09:14","modified_gmt":"2024-03-08T03:09:14","slug":"gks-2021-round-b","status":"publish","type":"post","link":"https:\/\/blog.cruciferslab.net\/?p=625","title":{"rendered":"GKS 2021 Round B"},"content":{"rendered":"\n<p>\u4e4b\u524d\u6211\u63d0\u904e\u9019\u7cfb\u5217\u89e3\u984c\u7b46\u8a18\u539f\u672c\u662f\u8981\u5728 GKS Round A \u6642\u5c31\u958b\u59cb\u5beb\u7684\uff0c\u65e2\u7136 Round B \u53ef\u4ee5\u4e0a\u5834\u4e86\u90a3\u5c31\u4f86\u5beb\u5427\u3002<\/p>\n\n\n\n<p>\u5148\u63d0\u4e00\u4e0b\uff1a\u63a5\u4e0b\u4f86\u7684 GKS \u6211\u4e0d\u6703\u5168\u90e8\u53c3\u52a0\uff1b\u73fe\u5728\u5df2\u7d93\u77e5\u9053\u7684\u662f\u81f3\u5c11\u4e03\u6708\u7684 Round D \u8209\u884c\u7684\u6642\u9593\u6b63\u597d\u6211\u6703\u6bd4\u8f03\u5fd9\uff0c\u6240\u4ee5\u90a3\u4e00\u56de\u78ba\u5b9a\u4e0d\u53c3\u52a0\u3002\u5176\u4ed6\u56de\u5c31\u770b\u6211\u90a3\u500b\u6642\u9593\u6709\u6c92\u6709\u7a7a\u4e86\u3002<\/p>\n\n\n\n<p>\u5206\u6578\u622a\u5716\u4ee5\u4e0b\u958b\u59cb\u6709\u96f7\u3002(\u5c0d\uff0c\u9019\u5f35\u622a\u5716\u662f\u5728\u7d50\u675f\u524d\u534a\u5c0f\u6642\u6642\u622a\u7684 XD \u8cfd\u5f8c\u7684\u540d\u6b21\u662f 164 \u540d\uff0c\u679c\u7136 Q4 +4 \u592a\u50b7\u4e86\u2026\u2026)<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"153\" src=\"https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/04\/image-1-1024x153.png\" alt=\"\" class=\"wp-image-626\" srcset=\"https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/04\/image-1-1024x153.png 1024w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/04\/image-1-300x45.png 300w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/04\/image-1-150x22.png 150w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/04\/image-1-768x114.png 768w, https:\/\/blog.cruciferslab.net\/wp-content\/uploads\/2021\/04\/image-1.png 1342w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">Q1. Increasing Substring<\/h2>\n\n\n\n<p>\u679c\u7136\u662f GKS \u7684\u96e3\u5ea6\uff0c\u7b2c\u4e00\u984c\u662f\u9001\u5206\u984c\u6240\u4ee5\u5c31\u4e0d\u591a\u8aaa\u4e86\uff0c\u53ea\u63d0\u4e00\u500b\u662f\u9019\u984c\u7684\u505a\u6cd5\u662f DP \u7684\u57fa\u672c\u578b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q3. Consecutive Primes<\/h2>\n\n\n\n<p>Q2 \u7531\u65bc\u7b49\u4e00\u4e0b\u6703\u63d0\u7684\u539f\u56e0\u6c7a\u5b9a\u665a\u9ede\u5beb\uff0c\u6240\u4ee5\u5148\u8df3\u4f86\u5beb Q3\u3002<\/p>\n\n\n\n<p>\u9019\u984c\u6bd4\u8f03\u6709\u554f\u984c\u7684\u5176\u5be6\u662f\u503c\u57df\u4f30\u8a08\u3002\u5927\u6e2c\u8cc7\u6709\u5230 10<sup>18<\/sup> \u7684\u5927\u5c0f\uff0c\u56e0\u6b64\u6211\u5011\u6703\u9700\u8981\u5224\u65b7\u5927\u7d04\u662f 10<sup>9<\/sup> \u5927\u5c0f\u7684\u6578\u662f\u5426\u70ba\u8cea\u6578\uff0c\u56e0\u6b64\u9700\u8981\u5efa\u7acb\u81f3\u5c11\u5230\u4e09\u842c\u591a\u7684\u8cea\u6578\u8868\uff1b\u6bd4\u8f03\u9ebb\u7169\u7684\u662f\u9019\u88e1\u4e0d\u80fd\u5beb\u6b7b\u4e00\u500b \\(\\lfloor\\sqrt{10^9}\\rfloor=31622\\)\u7684\u4e0a\u9650\uff0c\u56e0\u70ba\u53ef\u80fd\u6703\u9700\u8981\u5224\u65b7\u7a0d\u5fae\u5927\u65bc 10<sup>9<\/sup> \u7684\u6578\u7684\u7684\u8cea\u6578\u6027\u3002\u9019\u6709\u5169\u500b\u8fa6\u6cd5\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5c31\u76f4\u63a5\u4efb\u610f\u5b9a\u4e00\u500b\u5927\u4e0d\u5c11\u7684\u7bc4\u570d\u5efa\u8868\uff0c\u4f8b\u5982\u5341\u842c\uff1b<\/li>\n\n\n\n<li>\u7b97\u51fa\u6211\u5011\u53ef\u80fd\u6703\u6c42\u5230\u591a\u5927\u7684\u8cea\u6578\uff0c\u7528\u90a3\u500b\u63a8\u4e0a\u9650\u3002\u7531\u65bc\u4e0b\u9762\u8a08\u7b97\uff0c\u6211\u5011\u9802\u591a\u6703\u5f80\u5f8c\u627e 10<sup>9<\/sup> \u4e4b\u5f8c\u7684\u4e00\u500b\u8cea\u6578\uff1b\u9019\u4e00\u500b\u8cea\u6578\u662f \\(10^9+7\\) (\u5404\u4f4d\u5237\u904e\u4e0d\u5c11\u984c\u76ee\u7684\u4e00\u5b9a\u5e38\u5e38\u770b\u904e\u9019\u500b\u6578 XD)\uff0c\u6240\u4ee5\u958b\u6839\u865f\u7684\u4f30\u8a08\u503c\u5176\u5be6\u6c92\u5dee\u5f88\u591a\uff0c\u56e0\u6b64 31622 \u7684\u4e0a\u9650\u4e8b\u5be6\u4e0a\u662f\u53ef\u4ee5\u6cbf\u7528\u7684\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u5be6\u969b\u8a08\u7b97\u5247\u76f8\u5c0d\u7c21\u55ae\uff1a\u5728\u8f38\u5165\u503c Z \u7684\u5e73\u65b9\u6839\u9644\u8fd1\u627e\u6bd4\u5b83\u5927\u7684\u4e00\u500b\u8cea\u6578\u548c\u6bd4\u5b83\u5c0f\u7684\u5169\u500b\u8cea\u6578\uff0c\u7b54\u6848\u4e00\u5b9a\u662f\u9019\u4e09\u500b\u8cea\u6578\u4e4b\u9593\u7684\u5169\u500b\u4e58\u7a4d\u4e4b\u4e00\u3002\u627e\u7684\u65b9\u6cd5\u4e5f\u4e0d\u7528\u592a\u9ebb\u7169\uff0c\u4e00\u500b\u4e00\u500b\u627e\u904e\u53bb\u5224\u65b7\u662f\u5426\u8cea\u6578\u5c31\u597d\u4e86\u3002\u8cea\u6578\u5b9a\u7406\u544a\u8a34\u6211\u5011\u5e73\u5747\u53ea\u8981\u8a66 \\(O(\\log n)\\) \u500b\u6578\u5c31\u80fd\u627e\u5230 \\(n\\) \u9644\u8fd1\u7684\u4e0b\u4e00\u500b\u8cea\u6578\uff0c\u56e0\u6b64\u9019\u88e1\u7684\u5e73\u5747\u8a62\u554f\u662f\u5426\u8cea\u6578\u6b21\u6578\u662f \\(O(\\log n)\\)\uff0c\u6bcf\u6b21\u8a62\u554f\u4e5f\u82b1 \\(O(\\log n)\\) \u6b21\u9664\u6cd5\uff0c\u6240\u4ee5\u4e00\u500b\u56de\u7b54\u7684\u6642\u9593\u662f \\(O((\\log n)^2)\\)\uff0c\u4ee3\u5165 \\(n=\\sqrt{Z}\\) \u5373\u662f \\(O((\\log Z)^2)\\)\uff0c\u5f88\u5bb9\u6613\u5c31\u80fd\u5b8c\u6210\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q4. Truck Delivery<\/h2>\n\n\n\n<p>\u7c21\u8ff0\u4e00\u4e0b\u984c\u76ee\u662f\u9019\u6a23\u7684\uff1a<\/p>\n\n\n\n<p>\u6709\u4e00\u500b N \u500b\u9ede\u7684\u6a39\u5f62\u5716\uff0c\u6bcf\u500b\u908a\u4e0a\u6709\u500b\u300c\u8f09\u91cd\u9650\u5236\u300d\u8ddf\u300c\u82b1\u8cbb\u300d\uff1b\u73fe\u5728\u554f Q \u500b\u554f\u984c\uff0c\u6bcf\u500b\u554f\u984c\u662f\u7d66\u5b9a\u6a39\u4e0a\u4e00\u9ede\u548c\u4e00\u500b\u91cd\u91cf\uff0c\u6c42\u7531\u9019\u4e00\u9ede\u5230 1 \u865f\u9ede\u7684\u7c21\u55ae\u8def\u5f91\u4e2d\uff0c\u6240\u6709\u6bd4\u9019\u500b\u91cd\u91cf\u5927\u7684\u8f09\u91cd\u9650\u5236\u7684\u908a\u4e0a\u7684\u82b1\u8cbb\uff0c\u5176\u6700\u5927\u516c\u56e0\u6578\u503c\u3002<\/p>\n\n\n\n<p>\u9019\u500b\u6558\u8ff0\u88e1\u6700\u986f\u773c\u7684\u5c31\u662f\u9019\u500b\u300c\u6700\u5927\u516c\u56e0\u6578\u300d\u4e86\uff0d\uff0d\u4f46\u662f\u5176\u5be6\u9019\u53ea\u662f\u62ff\u4f86\u552c\u4f60\u7684\u6771\u897f\uff0c\u9019\u984c\u771f\u6b63\u7684\u96e3\u95dc\u662f\u5728\u5176\u4ed6\u7684\u7d30\u7bc0\u88e1\u3002\u5c31\u5148\u4f86\u7c21\u55ae\u8003\u616e\u4e00\u4e0b\u5927\u81f4\u4e0a\u9019\u984c\u8981\u600e\u9ebc\u505a\u597d\u4e86\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6240\u6709\u554f\u984c\u7684\u8def\u7dda\u7d42\u9ede\u662f\u4e00\u6a23\u7684\uff0c\u90fd\u662f 1 \u865f\u9ede\uff0c\u6240\u4ee5\u5176\u5be6\u53ef\u4ee5\u53cd\u904e\u4f86\uff0c\u5f9e 1 \u865f\u9ede\u51fa\u767c\uff0c\u6c42\u51fa\u5404\u500b\u9ede\u8981\u5f80\u54ea\u8d70\u624d\u6703\u8d70\u5230 1 \u865f\u9ede\uff1b<\/li>\n\n\n\n<li>\u6bcf\u500b\u554f\u984c\u4e00\u9032\u4f86\uff0c\u5c31\u6cbf\u8457\u7d00\u9304\u4e0b\u4f86\u7684\u8def\u7dda\u908a\u8d70\u908a\u554f\u908a\u6574\u7406\u5373\u53ef\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u9019\u6a23\u5dee\u4e0d\u591a\u5c31\u80fd\u904e\u5c0f\u6e2c\u8cc7\u4e86\uff0c\u4f46\u5927\u6e2c\u8cc7\u6703\u5728\u9019\u88e1\u9001\u4f60\u4e00\u500b TLE\u3002\u554f\u984c\u5728\u65bc\uff0c\u9019\u500b\u505a\u6cd5\u6bcf\u500b\u554f\u984c\u8981\u82b1 \\(O(N)\\) \u7684\u6642\u9593\u56de\u7b54\uff0c\u6240\u4ee5 Q \u500b\u554f\u984c\u7e3d\u8a08\u8981\u82b1 \\(O(QN)\\) \u6642\u9593\u3002\u89e3\u6c7a\u9019\u500b\u554f\u984c\u9700\u8981\u62ff\u7a7a\u9593\u63db\u6642\u9593\uff0c\u4e5f\u5c31\u662f\u6211\u5011\u9700\u8981\u591a\u7b97\u4e00\u9ede\u6771\u897f\u8a18\u4e0b\u4f86\uff0c\u554f\u984c\u4f86\u4e86\u5c31\u53ef\u4ee5\u82b1\u5c11\u65bc \\(O(N)\\) \u7684\u6642\u9593\u56de\u7b54\u3002<\/p>\n\n\n\n<p>\u65e2\u7136\u554f\u984c\u5728\u6bcf\u6b21\u8981\u82b1 \\(O(N)\\) \u6b65\u624d\u80fd\u6c42\u5b8c\uff0c\u90a3\u5c31\u628a\u9019 \\(O(N)\\) \u6b65\u5148\u7b97\u5b8c\u5427\uff01\u65bc\u662f\u6bcf\u500b\u9ede\u984d\u5916\u7d00\u9304\u5f9e\u9019\u88e1\u51fa\u767c\u591a\u91cd\u7684\u8ca8\u7269\u7684\u6700\u5927\u516c\u56e0\u6578\u591a\u5c11\u3002\u8ca8\u7269\u91cd\u91cf\u6700\u5927\u96d6\u7136\u662f \\(2\\times10^5\\)\uff0c\u4f46\u6211\u5011\u4e0d\u9700\u8981\u8a18\u4e0b\u6bcf\u500b\u91cd\u91cf\uff1a\u56e0\u70ba\u8def\u7dda\u6709\u9650\u9577\u7684\u95dc\u4fc2\uff0c\u53ea\u9700\u8981\u8a18\u591a\u91cd\u5230\u591a\u91cd\u7d50\u679c\u662f\u591a\u5c11\u5373\u53ef\uff1b\u7136\u5f8c\u56e0\u70ba\u9019\u500b\u91cd\u91cf\u7bc4\u570d\u662f\u9023\u7e8c\u7684\uff0c\u6211\u5011\u751a\u81f3\u4e0d\u9700\u8981\u8a18\u4e0a\u754c\uff0c\u53ea\u8981\u8a18\u4e0b\u754c\u5c31\u597d\u3002\u56e0\u6b64\u6bcf\u500b\u9ede\u7d00\u9304\u7684\u6771\u897f\u5c31\u6703\u8b8a\u6210\u985e\u4f3c\uff1a\u91cd\u91cf 0 \u8d77\u7d50\u679c\u70ba 0\uff0c\u91cd\u91cf 2 \u8d77\u7d50\u679c\u70ba 4\uff0c\u91cd\u91cf 6 \u8d77\u7d50\u679c\u70ba 2\uff0c\u7b49\u7b49\u9019\u6a23\u7684\u7d50\u679c\u3002\u66f4\u65b0\u7684\u6642\u5019\u4e8c\u5206\u641c\u5c0b\u627e\u5230\u6240\u8981\u7684\u76ee\u6a19\uff0c\u628a\u90a3\u500b\u7bc4\u570d\u5207\u958b\uff0c\u66f4\u65b0\u6240\u6709\u6bd4\u5b83\u91cd\u7684\u7d00\u9304\u5c31\u884c\u4e86\uff1b\u4f8b\u5982\u4f86\u4e86\u4e00\u500b\u91cd\u91cf\u9650\u5236 1 \u8cbb\u7528 5 \u7684\uff0c\u90a3\u5c31\u628a 0~2 \u9019\u4e00\u584a\u5207\u958b\uff0c1~2\u30012~6\u30016~\u221e \u5206\u5225\u548c 5 \u505a\u6700\u5927\u516c\u56e0\u6578\u66f4\u65b0\u5c31\u884c\u4e86\u3002<\/p>\n\n\n\n<p>\uff0d\uff0d\u7136\u5f8c\u5c31\u6703\u5403\u4e00\u500b MLE\u3002(\u5012) \u53ef\u4ee5\u77e5\u9053\uff0c\u9019\u6a23\u5b50\u7d00\u9304\u7684\u8cc7\u6599\u91cf\u6700\u591a\u662f\u6240\u6709\u9ede\u5230 1 \u865f\u9ede\u7684\u7c21\u55ae\u8def\u5f91\u9577\u5ea6\u548c\uff0c\u56e0\u70ba\u67d0\u500b\u9577\u5ea6\u7684\u8def\u5f91\u6700\u591a\u6709\u9019\u9ebc\u591a\u5206\u6bb5\u9ede\uff0c\u6bcf\u500b\u5206\u6bb5\u9ede\u90fd\u8981\u6709\u4e00\u500b\u7d00\u9304\u3002\u90a3\u9ebc\u7576\u6240\u6709\u8def\u5f91\u4e32\u6210\u4e00\u4e32\u6642\uff0c\u9019\u500b\u8def\u5f91\u9577\u5ea6\u548c\u5c31\u662f \\(O(N^2)\\)\uff0c\u518d\u7b97\u4e0a\u8981\u80fd\u4e8c\u5206\u641c\u63d2\u5165\u7684\u8cc7\u6599\u7d50\u69cb\u5f88\u5bb9\u6613\u5c31\u7206\u70b8\u4e86\u3002<\/p>\n\n\n\n<p>\u600e\u9ebc\u8fa6\uff1f\u610f\u5916\u5730\uff0c\u9019\u88e1\u6211\u5011\u9700\u8981\u56de\u5230\u6700\u4e00\u958b\u59cb\u984c\u76ee\u88e1\u90a3\u500b\u6700\u986f\u773c\u7684\u76ee\u6a19\uff1a\u6c42\u6700\u5927\u516c\u56e0\u6578\u3002\u5982\u679c\u984c\u76ee\u662f\u554f\u8cbb\u7528\u548c\u90a3\u5c31\u5b8c\u5168\u6c92\u8f12\uff0c\u4f46\u6700\u5927\u516c\u56e0\u6578\u4e0d\u4e00\u6a23\uff1a\u56e0\u70ba\u6240\u6c42\u5fc5\u9808\u662f\u7d66\u5b9a\u8cbb\u7528\u7684\u6700\u5927\u516c\u56e0\u6578\uff0c\u5f88\u6709\u6a5f\u6703\u5728\u66f4\u65b0\u6642\u597d\u5e7e\u500b\u5340\u9593\u7684\u7d50\u679c\u80fd\u5920\u5408\u4f75\u5728\u4e00\u8d77\u3002\u4e0a\u9762\u8209\u7684\u4f8b\u5b50\u5c31\u662f\u9019\u6a23\uff1a1~2 \u66f4\u65b0\u6210 5 \u4e86\u6c92\u932f\uff0c\u4f46 2~6 \u548c 6~\u221e \u90fd\u66f4\u65b0\u6210\u4e86 1\uff0c\u56e0\u6b64\u53ef\u4ee5\u5408\u4f75\u6210 2~\u221e \u7d50\u679c\u70ba 1\u3002\u9019\u6a23\u7684\u5408\u4f75\u5982\u679c\u554f\u7684\u662f\u8cbb\u7528\u548c\u90a3\u5c31\u5b8c\u5168\u4e0d\u53ef\u80fd\u767c\u751f\u3002<sup data-fn=\"02d92d49-f691-4e4f-beed-24d31a7fb56e\" class=\"fn\"><a href=\"#02d92d49-f691-4e4f-beed-24d31a7fb56e\" id=\"02d92d49-f691-4e4f-beed-24d31a7fb56e-link\">1<\/a><\/sup><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Q2. Longest Progression<\/h2>\n\n\n\n<p>\u9019\u88e1\u6211\u5148\u63d0\u4e00\u4e0b\u6211\u5f8c\u534a\u5834\u7684\u89e3\u984c\u9806\u5e8f\u3002\u5728 Q1 \u548c Q3 \u505a\u5b8c\u4e4b\u5f8c\u6211\u5176\u5be6\u662f\u5148\u505a Q4\uff0c\u4e3b\u8981\u539f\u56e0\u662f\u4e00\u4e0b\u5b50\u6c92\u6709\u5f88\u660e\u78ba\u7684 Q2 \u89e3\u6cd5\uff0c\u4f46 Q4 \u5df2\u7d93\u6709\u4e86\u4e0a\u9762\u90a3\u4e00\u7bc0\u7684\u524d\u534a\u90e8\u4efd\u7684\u60f3\u6cd5\u4e86\u3002\u5beb\u5b8c\u4e4b\u5f8c\u4e0a\u50b3\u6642\u624d\u56de\u982d\u4f86\u597d\u597d\u60f3\u4e86\u4e00\u4e0b Q2 \u7684\u505a\u6cd5\uff0c\u5beb\u4e86\u4e00\u500b\u534a\u89e3\u50b3\u4e0a\u53bb\uff1b\u9019\u6642 Q4 \u7684\u90a3\u500b\u4e0a\u50b3\u624d\u56de\u5831\u4e0a\u6bb5\u524d\u534a\u63d0\u5230\u7684 TLE\uff0c\u4e0d\u904e\u65e2\u7136 Q2 \u9019\u908a\u5df2\u7d93\u6709\u4e86\u4e00\u534a\u60f3\u6cd5\uff0c\u8a8d\u771f\u601d\u8003\u4e86\u4e00\u6703\u7e3d\u7b97\u662f\u77e5\u9053\u8981\u600e\u9ebc\u6539\u4e86\uff0c\u6240\u4ee5\u6539\u597d\u4e0a\u50b3\u904e\u4e86\u4e4b\u5f8c\u9019\u624d\u56de\u53bb\u628a Q4 \u88dc\u5b8c\u7684\u3002<\/p>\n\n\n\n<p>\u70ba\u4ec0\u9ebc\u4e00\u958b\u59cb\u6c92\u6709\u60f3\u6cd5\uff1f\u4e3b\u8981\u662f\u6c92\u6709\u6293\u4f4f\u300c\u8981\u6539\u54ea\u4e00\u500b\u300d\u7684\u554f\u984c\u3002\u4e00\u500b\u5f88\u660e\u986f\u7684\u9ede\u662f\uff0c\u8981\u6539\u5c31\u8981\u60f3\u8fa6\u6cd5\u628a\u5169\u500b\u7b49\u5dee\u6578\u5217\u7d66\u63a5\u5728\u4e00\u8d77\uff1a\u53c3\u8003\u8f38\u5165\u7684\u7b2c\u4e8c\u7d44\u662f\u4e00\u7a2e (\u628a\u5169\u500b 5 \u4e32\u7d66\u63a5\u8d77\u4f86)\uff0c\u4f46\u4e3b\u8981\u662f\u50cf 3 4 5 6 0 8 9 10 11 \u9019\u7a2e\uff0c\u628a 0 \u6539\u6210 7 \u63a5\u8d77\u5169\u500b\u7b49\u5dee\u6578\u5217\u9019\u7a2e\u72c0\u6cc1\u3002\u56e0\u6b64\u5f88\u81ea\u7136\u7684\u6703\u53bb\u7d00\u9304\u300c\u5230\u54ea\u88e1\u7684\u7b49\u5dee\u6578\u5217\u9577\u5ea6\u300d\uff0d\uff0d\u9019\u500b\u64cd\u4f5c\u5176\u5be6\u6211\u5011\u5728 Q1 \u5c31\u5df2\u7d93\u5be6\u4f5c\u904e\u4e00\u6b21\u4e86\uff0c\u6240\u4ee5\u5c31\u62ff\u4f86\u7528\u5427\u3002(\u9019\u5c31\u662f\u70ba\u4ec0\u9ebc\u6211\u7279\u5225\u5728\u4e0a\u9762 Q1 \u90a3\u88e1\u63d0 DP\uff0c\u56e0\u70ba\u540c\u4e00\u500b DP \u53ef\u4ee5\u7528\u5728\u9019\u4e00\u984c\u4e0a)<\/p>\n\n\n\n<p>\u90a3\u9ebc\u554f\u984c\u4f86\u4e86\uff1a\u8981\u600e\u9ebc\u63a5\uff1f\u4e26\u4e0d\u662f\u6bcf\u4e00\u7d44\u8f38\u5165\u90fd\u80fd\u628a\u5169\u4e32\u6578\u5217\u63a5\u8d77\u4f86\u7684\u3002\u6211\u5728\u9019\u88e1\u7a0d\u5fae\u82b1\u4e86\u9ede\u6642\u9593\u78ba\u8a8d\u5206\u985e\uff0c\u6574\u7406\u51fa\u4f86\u7684\u6709\u9019\u4e9b\u60c5\u5f62\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5ef6\u4f38\uff1a\u4f8b\u5982\u53c3\u8003\u8f38\u5165\u7b2c\u4e09\u7d44\u3002\u9019\u5c0d\u4efb\u4f55\u5df2\u6709\u7684\u7b49\u5dee\u6578\u5217\u90fd\u80fd\u7528\uff0c\u53ea\u8981\u6709\u7a7a\u9593\u7d66\u5b83\u5ef6\u4f38\u5c31\u884c\u4e86\u3002<\/li>\n\n\n\n<li>\u6578\u5217\u8de8\u904e\u6539\u52d5\u7684\u6578\u63a5\u4e0a\u53e6\u4e00\u500b\u6578\u5217\uff1a\u9019\u662f\u4e0a\u9762\u63d0\u7684\u63a5\u6578\u5217\u3002<\/li>\n\n\n\n<li>\u6578\u5217\u8de8\u904e\u6539\u52d5\u7684\u6578\u63a5\u4e0a\u4e00\u500b\u6578\uff1a\u9019\u662f\u5728\u5169\u908a\u7684\u6578\u5217\u7684\u516c\u5dee\u63a5\u4e0d\u8d77\u4f86\uff0c\u53ea\u6709\u9996\u9805\u80fd\u63a5\u7684\u6642\u5019\uff1b\u4f8b\u5982 4 5 6 0 8 10 \u9019\u6a23\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u65bc\u662f\u6211\u5beb\u4e00\u534a\u7684\u505a\u6cd5\u5373\u662f\u4ee5\u5df2\u77e5\u6578\u5217\u70ba\u4e3b\uff0c\u5617\u8a66\u5f80\u524d\u63a5\u770b\u80fd\u4e0d\u80fd\u63a5\u5230\u524d\u9762\u5176\u4ed6\u6578\u5217\u3002\u96d6\u7136\u81ea\u8a8d\u5beb\u8d77\u4f86\u6c92\u554f\u984c\uff0c\u4f46\u53ef\u80fd\u662f\u4e2d\u9593\u54ea\u500b\u689d\u4ef6\u6c92\u78ba\u8a8d\u597d\uff0c\u50b3\u4e0a\u53bb\u5403\u4e86\u4e00\u500b WA\u2026\u2026\u3002\u518d\u8a8d\u771f\u60f3\u4e86\u60f3\u4e4b\u5f8c\u624d\u60f3\u5230\u8aaa\uff1a\u6211\u70ba\u4ec0\u9ebc\u8981\u53bb\u5206\u6790\u6578\u5217\uff0c\u76f4\u63a5\u8003\u616e\u6211\u6539\u9019\u500b\u4f4d\u7f6e\u7684\u6578\u80fd\u5920\u63a5\u591a\u9577\u5c31\u597d\u5566\u3002\u6240\u4ee5\u6700\u5f8c\u901a\u904e\u7684\u505a\u6cd5\u662f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5c0d\u4e0d\u662f\u4e2d\u9593\u7684\u4f4d\u7f6e\uff0c\u5148\u628a\u9019\u500b\u4f4d\u7f6e\u5169\u908a\u5169\u500b\u6578\u7d66\u63a5\u8d77\u4f86\u3002\u5982\u679c\u7121\u6cd5\u7528\u6574\u6578\u63a5\u5c31\u4e0d\u7ba1\u9019\u500b\u4f4d\u7f6e\u4e86\u3002<\/li>\n\n\n\n<li>\u7136\u5f8c\u6aa2\u67e5\u9019\u6a23\u63a5\u8d77\u4f86\u4e4b\u5f8c\u5169\u908a\u539f\u6709\u7684\u7b49\u5dee\u6578\u5217\u80fd\u4e0d\u80fd\u9023\u8d77\u4f86\u3002\u70ba\u6b64\uff0c\u4e0a\u9762\u63d0\u5230\u7684 DP \u6b63\u53cd\u5169\u500b\u65b9\u5411\u6211\u90fd\u5148\u5404\u505a\u4e00\u6b21\u5b58\u8d77\u4f86\u3002<\/li>\n\n\n\n<li>\u80fd\u9023\u8d77\u4f86\u7684\u624d\u4f86\u8a08\u7b97\u7e3d\u9577\u5ea6\uff0c\u627e\u51fa\u6700\u5927\u503c\u3002<\/li>\n\n\n\n<li>\u5ef6\u4f38\u7684\u72c0\u6cc1\u600e\u9ebc\u8fa6\uff1f\u56e0\u70ba\u5ef6\u4f38\u5c0d\u4efb\u4f55\u5df2\u6709\u7684\u7b49\u5dee\u6578\u5217\u90fd\u80fd\u7528\uff0c\u6240\u4ee5\u5728 DP \u505a\u5b8c\u4e4b\u5f8c\u5c31\u5148\u627e\u51fa\u6700\u9577\u6578\u5217\u9577\u5ea6\u52a0\u4e00\u7576\u57fa\u5e95\uff0c\u7136\u5f8c\u624d\u505a\u4e0a\u9762\u3002\u9019\u4e5f\u662f\u70ba\u4ec0\u9ebc\u4e0a\u9762\u53ef\u4ee5\u76f4\u63a5\u8003\u616e\u5169\u908a\u63a5\u8d77\u4f86\u7684\u72c0\u6cc1\uff0c\u56e0\u70ba\u53ea\u63a5\u4e00\u908a\u4ee3\u8868\u9019\u662f\u500b\u5ef6\u4f38\uff0c\u6211\u5011\u5df2\u7d93\u8003\u616e\u5b8c\u4e86\uff1b\u5982\u679c\u4e2d\u9593\u63a5\u8d77\u4f86\u4e86\u4f46\u5169\u908a\u7684\u5df2\u6709\u7b49\u5dee\u6578\u5217\u90fd\u63a5\u4e0d\u4e0a\u4e5f\u4e0d\u7528\u8655\u7406\uff0c\u56e0\u70ba\u9019\u6a23\u6703\u5f97\u5230\u4e00\u500b\u9577\u5ea6 3 \u6578\u5217\uff0c\u4f46\u9019\u88e1\u6700\u9577\u6578\u5217\u9577\u5ea6\u52a0\u4e00\u81f3\u5c11\u662f 3\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u6642\u9593\u8907\u96dc\u5ea6\u662f\u8f15\u9b06\u901a\u904e\u7684 \\(O(N)\\)\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7e3d\u7d50<\/h2>\n\n\n\n<p>\u5176\u5be6\u9019\u5834\u6211\u4e00\u958b\u59cb\u4ee5\u70ba\u662f\u9031\u65e5\u665a\u4e0a\u5341\u4e00\u9ede\u958b\u8cfd\u3002(\u7206) \u7576\u521d\u5728\u6211\u7684\u884c\u4e8b\u66c6\u4e0a\u8a18\u6642\u9593\u6642\u5fd8\u8a18\u958b UTC+8 \u4e86\uff0c\u6240\u4ee5\u8a18\u5230\u4e86 UTC \u6642\u9593\uff1b\u9031\u65e5\u665a\u4e0a\u8981\u6e96\u5099\u958b\u5834\u6642\u624d\u767c\u73fe\u641e\u932f\u4e86\u3002\u65bc\u662f\u534a\u591c<s>\u6478\u9b5a<\/s>\u5beb\u53e6\u4e00\u7bc7\u6587\u7ae0\u5beb\u4e86\u4e00\u500b\u665a\u4e0a\u4e4b\u5f8c\u65e9\u4e0a\u4e03\u9ede\u958b\u8cfd\uff0c\u8166\u888b\u6709\u9ede\u5361\u5361\u4e86\u6240\u4ee5\u624d\u6703\u5728 Q2 \u9019\u7a2e\u984c\u76ee\u5361\u95dc\u2026\u2026.\u3002<\/p>\n\n\n\n<p>\u7136\u5f8c\u9084\u6709\u4e00\u4ef6\u9019\u4e09\u5834\u4e0b\u4f86\u6ce8\u610f\u5230\u7684\u4e8b\uff1a\u6700\u8fd1\u7684\u984c\u76ee\u8d8a\u4f86\u8d8a\u559c\u6b61\u6253\u7834 2<sup>32<\/sup> \u7684\u7bc4\u570d\u4e86\u2026\u2026\u5305\u542b\u9019\u4e00\u5834\uff0c\u6211\u5176\u5be6\u597d\u5e7e\u6b21\u9001\u4e0a\u53bb WA \u7684\u539f\u56e0\u662f\u5fd8\u8a18\u4e00\u4e9b\u503c\u80fd\u5920\u8d85\u904e\u9019\u500b\u7bc4\u570d\u6240\u4ee5\u7528\u4e86 32-bit \u7684 <code>int<\/code> \u4f86\u88dd\u3002\u561b\u9084\u597d\u73fe\u5728\u5df2\u7d93\u4e0d\u662f\u5341\u4e94\u5e74\u524d\u90a3\u7a2e\u9023 <code>long long<\/code> \u90fd\u8981\u6e2c\u80fd\u4e0d\u80fd\u7528\u7684\u6642\u4ee3\uff0c<code>int64_t<\/code> \u5728\u5404\u5927\u7de8\u8b6f\u5668\u90fd\u5df2\u7d93\u652f\u63f4\u4e86\uff0c\u52a0\u4e0a C++ \u8f38\u51fa\u4e0d\u7528\u5beb\u683c\u5f0f\u5b57\u4e32\u6240\u4ee5\u7528\u8d77\u4f86\u6bd4\u4ee5\u524d\u65b9\u4fbf\u5f88\u591a\u4e86\u3002<\/p>\n\n\n\n<p>\u4e0b\u4e00\u5834\u4e94\u6708\u4e2d\u7684 GCJ R2 \u518d\u898b\uff5e<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u8a3b\u8173<\/h2>\n\n\n<ol class=\"wp-block-footnotes\"><li id=\"02d92d49-f691-4e4f-beed-24d31a7fb56e\">\u4e8b\u5be6\u4e0a\u7531\u65bc\u5c0f\u65bc\u7b49\u65bc \\(10^{18}\\) \u7684\u6700\u5927\u7684<a href=\"https:\/\/zh.wikipedia.org\/wiki\/%E9%AB%98%E5%90%88%E6%88%90%E6%95%B0\">\u9ad8\u5408\u6210\u6578<\/a>\u662f 74,801,040,398,884,800\uff0c\u5176\u6709 64,512 \u500b\u56e0\u6578\uff0c\u548c\u6211\u5011\u7684 \\(N\\) \u76f8\u7576\uff0c\u56e0\u6b64\u6e2c\u8cc7\u5176\u5be6\u662f\u53ef\u4ee5\u5f88\u904e\u4efd\u5730\u5168\u90e8\u51fa\u9019\u500b\u9ad8\u5408\u6210\u6578\u7684\u56e0\u6578\uff1b\u597d\u5728\u9019\u4e0d\u662f GCJ\uff0c\u6c92\u6709\u9019\u9ebc\u904e\u4efd\u7684\u6e2c\u8cc7\u5b58\u5728 (\u7b11) \u9019\u984c\u7684\u5b98\u65b9\u984c\u89e3\u662f\u7528\u4e86\u7dda\u6bb5\u6a39\u505a\u96e2\u7dda\u67e5\u8a62\uff0c\u8a73\u60c5\u5c31\u81ea\u884c\u53c3\u8003\u5b98\u65b9\u984c\u89e3\u5427\uff1b\u7528\u7dda\u6bb5\u6a39\u7684\u8a71\u5373\u4f7f\u984c\u76ee\u662f\u554f\u8cbb\u7528\u548c\u4e5f\u80fd\u8f15\u9b06\u6c42\u51fa\u3002 <a href=\"#02d92d49-f691-4e4f-beed-24d31a7fb56e-link\" aria-label=\"\u8fd4\u56de\u8a3b\u8173\u53c3\u7167 1\">\u21a9\ufe0e<\/a><\/li><\/ol>","protected":false},"excerpt":{"rendered":"<p>\u4e4b\u524d\u6211\u63d0\u904e\u9019\u7cfb\u5217\u89e3\u984c\u7b46\u8a18\u539f\u672c\u662f\u8981\u5728 GKS Round A \u6642\u5c31\u958b\u59cb\u5beb\u7684\uff0c\u65e2\u7136 Round B \u53ef\u4ee5\u4e0a\u5834\u4e86\u90a3\u5c31 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"[{\"content\":\"\u4e8b\u5be6\u4e0a\u7531\u65bc\u5c0f\u65bc\u7b49\u65bc \\\\(10^{18}\\\\) \u7684\u6700\u5927\u7684<a href=\\\"https:\/\/zh.wikipedia.org\/wiki\/%E9%AB%98%E5%90%88%E6%88%90%E6%95%B0\\\">\u9ad8\u5408\u6210\u6578<\/a>\u662f 74,801,040,398,884,800\uff0c\u5176\u6709 64,512 \u500b\u56e0\u6578\uff0c\u548c\u6211\u5011\u7684 \\\\(N\\\\) \u76f8\u7576\uff0c\u56e0\u6b64\u6e2c\u8cc7\u5176\u5be6\u662f\u53ef\u4ee5\u5f88\u904e\u4efd\u5730\u5168\u90e8\u51fa\u9019\u500b\u9ad8\u5408\u6210\u6578\u7684\u56e0\u6578\uff1b\u597d\u5728\u9019\u4e0d\u662f GCJ\uff0c\u6c92\u6709\u9019\u9ebc\u904e\u4efd\u7684\u6e2c\u8cc7\u5b58\u5728 (\u7b11) \u9019\u984c\u7684\u5b98\u65b9\u984c\u89e3\u662f\u7528\u4e86\u7dda\u6bb5\u6a39\u505a\u96e2\u7dda\u67e5\u8a62\uff0c\u8a73\u60c5\u5c31\u81ea\u884c\u53c3\u8003\u5b98\u65b9\u984c\u89e3\u5427\uff1b\u7528\u7dda\u6bb5\u6a39\u7684\u8a71\u5373\u4f7f\u984c\u76ee\u662f\u554f\u8cbb\u7528\u548c\u4e5f\u80fd\u8f15\u9b06\u6c42\u51fa\u3002\",\"id\":\"02d92d49-f691-4e4f-beed-24d31a7fb56e\"}]"},"categories":[7,4],"tags":[],"class_list":["post-625","post","type-post","status-publish","format-standard","hentry","category-gcj","category-programming"],"_links":{"self":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/625","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=625"}],"version-history":[{"count":4,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/625\/revisions"}],"predecessor-version":[{"id":1749,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=\/wp\/v2\/posts\/625\/revisions\/1749"}],"wp:attachment":[{"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.cruciferslab.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}